Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12940 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
424 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19)(20,31)(21,36)(22,26)(23,41)(24,30)(25,32)(27,37)(28,39)(29,38)(33,48)(34,43)(35,47)(40,46)(42,44)(45,49);(14,16,17,15)(18,20)(19,25)(21,33)(22,40)(23,42)(24,35)(26,43)(27,44)(28,47)(29,48)(30,46)(31,36)(32,37)(34,38)(39,49)(41,45);(19,26)(21,37)(22,39)(23,38)(25,43)(27,30)(28,41)(29,36)(31,48)(32,33)(34,42)(40,49)(44,46)(45,47)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5928);